Long-time behavior of the heterogeneous SIRS epidemiological model

We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the coefficients, we prove that the solutions converge to an equilibrium that we identify and establish some estimates on the speed of propagation.